well some people claim Ulfric was fleeing Skyrim which is as groundless and unproven as calling him racist.
And you do see my point even if you don't agree with it. Even you question why would imperial soldiers march on Shor's Watchtower and wipe out the Rift guards? If not part of the trap to kill Ulfric, then why? Just like Balgruuf's sniveling steward who is paranoid sending troops to Riverwood would be perceived as an act of war on Falkreath, wouldn't an imperial attack on Riften guards seem like an act of war? The note can be found before the Civil War has been started, so saying the imperials were trying to take the hold is groundless. After all their camp is by the very path leading to Helgen. Very likely placed there to delay any Riften or Stormcloak soldiers from getting to Ulfric before Tullius got safely behind Helgen's walls.
Again, we don't know why Ulfric was in near Darkwater Crossing. We don't even know exactly what side of Darkwater Crossing he was on. He could have been towards the Mill, or up in the hills high above Darkwater Crossing. OR he could have been on the Eastmarch side in the hotsprings. Or he could have been between Darkwater Crossing and Shor's Stone/ Watchtower area. Because of the attack on the tower I'm more inclined to think he was in that area.
But, all this is speculation due to the simple fact an intro was slapped together without the writers perhaps really thinking it all through.